KMP Algorithm Achieves Linear-Time String Matching by Skipping Redundant Comparisons

The Knuth-Morris-Pratt (KMP) algorithm solves the classic computer science problem of pattern matching within a text string in O(N + M) time, far outperforming the brute-force O(N × M) approach. It achieves this efficiency by preprocessing the pattern into a data structure called the LPS (Longest Proper Prefix which is also a Suffix) array, which encodes information about partial matches. When a mismatch occurs during search, KMP uses the LPS array to skip ahead rather than restarting comparisons from scratch. The algorithm operates in two phases: building the LPS array in O(M) time and performing the actual text search in O(N) time, using only O(M) additional space. Its efficiency makes it well-suited for real-world applications such as search engines, code editors, plagiarism detection, and DNA sequence analysis.